| We show the termination of any log-minimal model program for a pair (X, D) of a projective irreducible symplectic manifold X and an effective R-divisor D. To prove the result we follow Shokurov’s strategy and show that LSC and ACC for mld’s hold for all the models appearing along any log-MMP of the initial pair. To establish ACC a crucial result, which may be interesting on its own, is a generalization to the singular setting of Huybrechts’ theorem on deformation equivalence of birational hyperkähler manifolds. |